Respuesta :
Answer:
a) V_avg = 5.33 m/s
b) flow(m_a) = 0.00084 kg/s
c) flow(m_f) = 5.63*10^-5 kg/s
d) m_f = 4.2225*10^-7 kg / cycle
Explanation:
Given:
- The rotation of crankshaft N = 8000 RPM
- The total volume displaced V_d = 6.28 cm^3
- The volumetric efficiency n_v = 0.85
- The Fuel to air ratio FA = 0.067
- Stroke length = Bore size
Find:
(a) Average piston speed. [m/sec]
(b) Flow rate of air into engine. [kg/see]
(c) Flow rate of fuel into engine. [kg/see]
(d) Fuel input for one cycle. [kg/cycle]
Solution:
- To compute the average piston speed we need the Stroke length of the engine. We will used the amount of volume displaced to calculate it:
V_d = A_b * S
V_d = pi*d^2*S / 4
Since, we know that stroke length and bore dia are equal hence S = d:
V_d = pi*S^3 / 4
- Input values:
6.28 = pi*S^3 / 4
S = cuberoot ( 7.9959)
S = 2.0 cm
- The average piston speed can now be calculated from the formula:
V_avg = S*N / 30
V_avg = 0.02*8000 / 30
V_avg = 5.33 m/s
- We can use the relation of volumetric efficiency to calculate the flow rate of air into the engine flow(m_a):
n_v = flow(m_a) / p_a*V_d*N
Where, p_a is the density of air at atmospheric conditions, using ideal gas law we can calculate:
p_a = P_atm / R*T_amb
Where. P_atm = 101 KPa , R = 0.287 KJ/kgK , T_amb = 25 + 273 = 298 K
p_a = 101 / 0.287*298 = 1.181 kg/m^3
Hence,
flow(m_a) = p_a*V_d*N*n_v
- Plug values in:
flow(m_a) = 1.181*6.28*10^-6*8000/60*.85
flow(m_a) = 0.00084 kg/s
- We will use the Fuel to Air ratio to compute the flow rate of fuel in a engine flow(m_f):
flow(m_f) = FA*flow(m_a)
- Plug in the values:
flow(m_f) = 0.067*0.00084
flow(m_f) = 5.63*10^-5 kg/s
- The fuel in put per cycle can be calculated as follows:
m_f = flow(m_f)*60 / N
- plug in values:
m_f = 5.63*10^-5*60 / 8000
m_f = 4.2225*10^-7 kg / cycle
